Question: Rewrite as a simplified fraction. ${1.8\overline{7} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 187.7777...\\ 10x &= 18.7777...\end{align*}}$ Subtracting the two equations, we have: ${90x = 169}$ ${x = \dfrac{169}{90}} \text{or} {1 \dfrac{79}{90}}$